Method and apparatus for end point detection in potentiometric titration

ABSTRACT

A method of automatically determining the end point of a potentiometric titration and apparatus for carrying out the method are disclosed. A titrant is added to a solution at a measured rate by a motor-driven burette. A counter and a count accumulator are provided to record the amount of titrant added to the sample and means are provided to measure changes in the pH of the sample as the titrant is added. The count representing the volume of titrant is recorded until a preset threshold point is reached, this point being determined by a voltage representing the first derivative of the changing pH potential in the sample. The occurrence of the threshold point changes the counter and count accumulator so that only one-half of the actual count is registered in the accumulator. The titration continues beyond the normal end point until the first derivative value returns to the threshold point, at which time the titration ends. The count in the accumulator at this time provides a direct reading of the volume of titrant added to the end point, thereby providing a fast and accurate determination of the end point. The half count technique is applicable to any titration that can be carried out by standard or developed potentiometric procedures.

United States Patent [1 1 Rothermel, Jr.

[ METHOD AND APPARATUS FOR END POINT DETECTION IN POTENTIOMETRICTITRATION [75] Inventor: Charles E. Rothermel, Jr.,

Waynesboro, Va.

[73] Assignee: Rothermel Associates, Inc.,

Waynesboro, Va.

22 Filed: Apr. 27, 1972 21 Appl. No.: 248,092

[52] US. Cl. 204/1 T, 23/230 R, 23/253 R OTHER PUBLICATIONS Phillips,Automatic Titrators, 1959, Academic Press, pp. 74-80.

dmv

dvol

[ Oct. 30, 1973 Primary Examiner-T. Tung Attorney-Harris C. Lockwood[57] ABSTRACT A method of automatically determining the end point ofa'potentiometric titration and apparatus for carrying out the method aredisclosed. A titrant is added to a solution at a measured rate by amotor-driven burette. A counter and a count accumulator are provided torecord the amount of titrant added to the sample and means are providedto measure changes in the pH of the sample as the titrant is added. Thecount representing the volume of titrant is recorded until a presetthreshold point is reached, this point being determined by a voltagerepresenting the first derivative of the changing pI-l potential in thesample. The occurrence of the threshold point changes the counter andcount accumulator so that only one-half of the actual count isregistered in the accumulator. The titration continues beyond the normalend point until the first derivative value returns to the thresholdpoint, at which time the titration ends. The count in the accumulator atthis time provides a direct reading of the volume of titrant added tothe end point, thereby providing a fast and accurate determination ofthe end point. The half count technique is applicable to any titrationthat can be carried out by standard or developed potentiometricprocedures.

44 Claims, 11 Drawing Figures -END POINT THRESHOLD VOL. OF TIT|RANTADDED PATENTEDUBI I973 SHEET 2 [IF 5 Q TOP REFILL BOTTOM "ij4gv LIMIT250 5 MOTOR I CONTROL 206 9/0 262 254 GATE 4 STIRRER MOTOR I CONTROL I2/4 GATE Dc POWER M4 /46 SUPPLY SGHMITT I I I TRIGGER FF -/50 2/0 "Z04/46--couNT 226 GATE I HOLD FF 203 D f INIT, FF DE L. FAST H s LOW RCONVERTER MOTOR L90 MOTOR ESTART AND COUNTER l I I sI.ow MOTOR DISPLAYIuNITsI' /80 A92 7 2/6 t 7 IIo'sI 3 208 l, 0EI IvERY /67 /74 7 iSELECTOR 6 2 PERMIT 478 SCHMITT /68 1 TRIGGER 208 /63 220 222 (IOOO'S)/84 FF FF HOLD COUNT COUNT o o l /225 2/8 226 PATENIEDucI 30 1915.769.178 SHEET 30F 5 FF coum CONTROL I48 WIFFI:

TRIGGER SGHMITT .r- /82 5 LOW MOTOR FF FAST MOTOR I 'GOUNT I 2 COUNTFULL COUNT METHOD AND APPARATUS FOR END POINT DETECTION INPOTENTIOMETRIC TITRATION BACKGROUND OF THE INVENTION The presentinvention relates, in general, to a system for detecting the end pointof a potentiometric titration, including both the method and apparatusfor carrying out such a procedure. More particularly, the inventionrelates to half count technique for obtaining direct indications of theexact volume of titrant delivered at the end point of a titrationprocedure, the indication being provided automatically, without the needfor laborious and time-consuming graphical analysis.

In the field of electroanalysis, wherein electrical variables areexperimentally controlled so as to produce an electrical responsedependent in some manner. upon the composition of a solution,- thegeneral use of potentiometric methods are well known. Potentiometryrefers to the use of the measured potential of a cell to determine asolution concentration, and in a potentiometric titration, the measuredcell potential is used to monitor the solution concentration of thesample species during the course of a titration involving that species.This type of analysis offers high accuracy because only relative changesin cell potential during the titration are important, and variations inabsolute values can be ignored. Numerous methods have been devised topermit detection of the end point and measurement of the amount oftitrant added in a potentiometric titration to be accomplishedautomatically. Present day automatic to the titrant delivered. Themeasured potential varia-' tions are automatically plotted on the chart,and by inspection of the curve so plotted, the entrance and exit of thesteep portion of the curve in whichthe inflection occurs can be located.By taking half the distance between these points, a close estimate ofthe end point can be obtained. One of the main advantages of anautomatic titrator is that a large number of similar titra tions can beperformed in a short period of time, but the requirement for manualdetermination of the end point in each case obviates this advantage. Inaddition, poor results can occur if there is a slow attainment ofequilibrium in the solution during the titration, or if the mixing rateis inadequate. This problem can be overcome to some extent by the use ofan anticipation technique wherein the rate of titrant addition isautomatically slowed as the equivalence point is approached; however,this does not entirely eliminate it, for the slower rate itselfintroduces errors and also reduces the advanta e of the automaticsystem. It should also be noted that in many titrations, the points ofinflection on the plotted curve are very difficult to locate with anyaccuracy, and this introduces further error in the measurements.

In the type of automatic titrator where a single volume reading isprovided to denote the equivalence point, it is usual to provide meansfor stopping the titrant flow at the end point, and to provide anindication of the total volume delivered. Normally such devices employ apotentiometer which is set at the end-point potential for the titrationso that when the cell potential equals or slightly exceeds the presentvoltage, a relay is actuated to stop titrant flow. An anticipationtechnique can also be used in conjunction with this method, so that asthe end point is approached, the flow of titrant is reduced. Such asystem generally performs very well in standard aqueous titrations;however, in practice it has been found that in organic and non-aqueoussolutions this type of system tends to fail. Such failures usually stemfrom the inevitable fluctuations in electrode potential caused by drift,noise, and general instability of the electrodes themselves. In order toovercome such problems, it has been the practice to utilize either thefirst derivative or the second derivative of the cell potential, ratherthan using the cell voltage directly. The use of asecond derivativesensing circuit has been favored since it has the advantage that theexact nature of the titration curve need not be known, and the form ofthe second derivative itself can be used to anticipate the end point andshut off titrant flow when its value becomes zero. However, the secondderivative is particularly susceptible to noise problems, for as thesecond derivative approaches the cut off point, superimposed noisesignals can either advance or delay the cut off of the titrant flow andthus invalidate the test.

SUMMARY OF THE INVENTION Accordingly, it is an object of the presentinvention to providean improved method and apparatus for determining theend point of a titration and for providing an automatic and accurateindication of the volume of titrant.

It is another object of the present invention to provide an automaticpotentiometric titration which will provide a direct and accurateindication of the volume of titrant added at an accurately determinedend point.

It is a further object of the present invention to provide an automaticpotentiometric titration which overcomes the problems encountered inprior devices whereby fast and accurate determinations of end points canbe carried out for a large-number of samples.

It is another object of the present invention to provide a method forconducting automatic potentiometric titrations without the need forproviding an arbi-- trary predetermined end point, and which eliminatesthe delays inherent in techniques which involve the manual plotting ofmeasured data.

In the numerous attempts that have been made in the past to produce anaccurate and reliable automatic potentiometric titrator, variousapproaches have been taken as generally outlined above, but none havebeen entirely satisfactory. For example, where samples taken from anindustrial process are to be titrated in order to provide a continuousmonitoring of the process, the use of a graphical analysis is totallyinadequate, for a considerable amount of time is required to study thecharts produced by the titrator and obtain a reading of the values. Thetitrators which work to a preset cell potential, and stop the titrationwhen that potential is reached, are unacceptable for such systems sincein nonaqueous and organic samples the titrations are not reproducibleand a large number of invalid tests can result from this approach.Similarly, the use of the second derivative in such systems increasesthe chance for error since the effects of noise and drift become moreevident as the rate of titration is slowed in an attempt to obtaingreater accuracy. However, it has been discovered that in any titrationin which there is a potentiometric break in the curve representing thecell potential as a sample is titrated through the end point of thetitration, a plot of the first derivative of that break will show anarea of symmetry about a predetermined, or threshold level. Even if thecurve isirregular or very broad, there will still be a portion of thefirst derivative curve that will be generally symmetrical above thethreshold value.

Since the peak of the first derivative curve occurs at the point ofmaximum change in the cell potential, which point is the end point, orequivalence point, to be determined, it will now be seen that thischaracteristic of symmetry in the first derivative can be utilized todetermine the end point of the titration. This is accomplished bymeasuring and accumulating a count correspondin g to the full volume'oftitrant added to a sample until the threshold value is reached;thereafter a count corresponding to one-half of the volume of titrantadded as the solution is overtitrated is accumulated, with the countstopping when the value of the first derivative returns to the thresholdvalue. The curve representing the first derivative of the pH variationis used to control the accumulation of one-half the measured volume oftitrant through the symmetrical portion of the curve, for it has beenfound that one-half of the total volume added during thisover-titration, taken with the full count accumulated up to thethreshold, will provide an accurate measure of the volume of titrantrequired to reach the midpoint of the derivative curve; i.e., to reachthe equivalence point of the titration. This method, which is referredto herein as the half-count technique, provides more precisemeasurements of titration than was possible with prior automaticdevices, giving an accuracy that was previously available only throughlaborious plotting of measured values and calculating the end point froma careful measurement of the slope of the curve so obtained.Furthermore, the present device is able to provide this accuracy withmuch greater speed and reliability than was previously thought possible,and eliminates the need for the highly trained technicians who wererequired, under such previous methods, to carry out the variouscalculations. 1

To perform the half-count procedure, the present invention utilizes astandard motor-driven syringe for adding titrant to a sample. A digitalcounter makes an accurate measure of the exact volume of titrantdispensed by the syringe and feeds this information to an appropriateaccumulator. Electrodes are provided in the sample being titrated, andelectrical circuit means are provided for obtaining the first derivativeof the potential measured by these electrodes. A motor-driven burette isoperated at a fast speed until a predetermined count representative of apredetermined volume of titrant added to the sample, is obtained; thespeed of the drive motor is then reduced so that the titrant is addedmore slowly, and when a selected threshold value of the first derivativevoltage is reached, the digital counter is modified so that onlyone-half of the measured count is fed to the accumulator. The titrationcontinues in this manner until the equivalence point is passed and thevalue of the first derivative returns to the threshold value, at whichtime the drive motor is turned off and the accumulator displays theaccumulated count. This count represents the actual volume of titrantadded to the sample to reach the equivalence point, thus providing anaccurate, fast readout of the result of the titration.

In a particular embodiment of the invention concept, the test samplesmay be taken from an industrial process at predetermined intervals andplaced in receptacles on a turntable. Suitable solvents may be added tothe test material, and the receptacles then indexed in turn to thetitrating station where the electrodes are lowered into the receptacle,a stirring bar is activated to agitate the sample and the titrationbegins. A predetermined quantity of titrant is added to the sample at avery rapid rate, under the control of a fast motor driving the burette.Thereafter, the motor is slowed down and the titrant added at a slowrate until the threshold value is reached. At this point, the volumemeasuring apparatus shifts to a half-count'and continues in this mannerthrough the end point until the titration is complete and the motor isstopped. The accumulated count indicating the volume required to reachthe equivalence point is then displayed or printed out, the electrodesare removed from the test sample, the sample is discarded and the nextsample is indexed into position.

Although the present application is directed to a system for carryingout a titration having a single break in the curve indicating therelationship between pH (voltage) and volume of titrant added, it willbe apparent from what follows that the process is equally applicable toa titration of a complex sample wherein two breaks occur in thetitration curve as the titrant is added. In these situations, the volumeadded between the equivalence point of the first break and that of thesecond break is the value of interest, and it therefore becomesnecessary to modify the counting mode of the measuring system. Thus, asthe first derivative curve increases above the threshold value for thefirst time, corresponding to the occurrence of the first break, ahalfcount is initiated. This continues until the curve falls below thethreshold value, at which time a full count begins until the thresholdis again exceeded at the second break. A half-count again is used untilthe first derivative falls below the threshold value for a second time,at which time the titration stops and the accumulated value isdisplayed, this value being the volume of titrant added from the endpoint of the first break to the end point of the second break.

BRIEF DESCRIPTION OF THE DRAWINGS The foregoing and additional objects,features and advantages, together with various modifications of thepresent invention will become evident from a consideration of thefollowing specification and claims, taken in conjunction with theaccompanying drawings, in which: 7

FIG. 1 is a diagrammatic illustration of a typical titration curve;

FIG. 2 is a diagrammatic illustration of curve representing the firstderivative of the titration curve of FIG.

FIG. 3 is a diagrammatic illustration of a curve representing the secondderivative of the curve of FIG. 1;

FIG. 4 is a diagrammatic illustration of a system for automatictitrationutilizing the half-count method of the present invention;

FIG. 5 is a more detailed illustration of the system of FIG. 4;

FIG. 6 is a circuit diagram of the count gate of the system of FIG. 5;

FIG. 7 is a circuit diagram of a typical OR gate usable in the circuitof FIG. 6;

FIGS. 8A and 8B comprise a diagrammatic'illustration of an expandedautomatic titrating system using the method of the present invention;and

FIGS. 9 and 10 disclose a typical double-break potentiometric curve andthe first derivative thereof, respectively.

DESCRIPTION OF PREFERRED EMBODIMENTS Turning now to a consideration ofFIG. 1, there is illustrated therein at 10 a typical titration curve ofthe type that is obtained in the conventional potentiometric titrationof any material that can be successfully subjected to analysis of thistype under standard and well-known potentiometric techniques. This curverepresents a plotting of the potential measured across a pair ofelectrodes immersed in the sample being tested, the potential being inmillivolts and proportional to the pH of the sample, versus the volumeof standard titrant added to the sample. Such curves are commonly usedto determine the end point of a titration, which is defined as being thepoint on the curve where the potential is changing most rapidly, and isindicated in the figure at 12. The illustration is of a titration inwhich the sample experiences a decreasing pH, resulting in a positive-going first derivative.

In a graphical determination of the end point, the entrance and exitpoints of the steep portion of the curve are determined by inspection,and one-half the distance between these points is taken as the bestestimate of the end point. Although this technique can producesatisfactory results when the curve is well defined, as in the exampleof FIG. 1, in many cases the slope of the curve may be somewhatirregular and poorly defined, and in such a situation it is oftennecessary to plot a large number of tangents to the curve and from theirpoints of intersection determine the desired point of maximum change.

Although the graphical method of end point determination can be veryaccurate, it will be apparent that it is also highly time consuming, andexperienced, highly trained personnel are required if good results areto be obtained. Although the plotting of the curve can be doneautomatically, the accurate determination ofthe end point is not welladapted to automation, and for this reason the art has turned to the useof mathematically or electrically obtained first derivativeor secondderivative cruves, such as those illustrated in FIGS. 2 and 3,respectively. As will be seen from the FIG; 2 illustration, the firstderivative 14 of the titration curve provides a peak at the area of thetitration curve wherein the pH is changing most rapidly, and thisprovides a highly accurate determination of the end point 16, in theory.Similarly, the second derivative 18 also provides a high degree oftheoretical accuracy in that the second derivative changes from anegative to a positive value at the desired endpoint. Although the useof first and second derivatives has increased the speed with which theresults of a potentiometric titration can be obtained, and hasfacilitated to some extent the automation of such systems, nevertheless,for a number of reasons, the theoretical accuracy of such techniques hasnot been obtained. For example, by the very nature of chemicalreactions, minor disturbances prevent the generation of an ideal curve,thus complicating the graphical determination and introducing errorsinto the derivative values. Further, the potential change in a givenreaction may exhibit an almost constant rate of change near the centerof the steep slope, thus preventing an accurate determination of thearea of maximum change either by a graphical method or by a firstderivative method. As will be seen from FIG. 3, the second derivativecrosses the zero axis two times, at 22 and 24, during the titration,with the second crossing 24 being at the point of interest. An automaticmachine made sensitive to this second crossing is particularlysusceptible to noise and interference; for example, on the downwardsloping portion of the curve, in the area of the zero crossing 22, noisecan superimpose an upward going signal which would cross the zero axisand trigger the sensing equipment before the actual end of the titrationis reached at point 24. Thus it has been extremely difficult'to devise amachine which will be sensitive to the exact end point of a titration,thereby to provide with the required degree of accuracy and speed anindication of the titrant added to a sample.

However, the present invention permits an accuracy of operationapproaching that of the theoretical values in an automatic machine. Thisaccuracy is based upon the recognition that virtually every firstderivative curve exhibits a high degree of symmetry about the end pointand above a determinable threshold level. This threshold level 'may varyfor different curves, but it has been found that a practical valuecan beestablished for a given type of titration with sufficient reliability topermit automatic and accurate determination of the end point by ahalf-count technique. Thus, the symmetry of the first derivative curveis such that as the first derivative curve increases above a thresholdlevel 26, as at point 28, passes through the end point 16 and declinesagain to the threshold level, as at point 30, the amount of titrantadded to the sample between points 28 and 30 may be divided in half tofind the amount of titrant added between point 28 and end point 16.Because of the symmetry, then, one-half the volume between the thresholdcross over points gives the value of the end point, and when this valueis added to the full amount of titrant metered into the sample to reachthe threshold value, the sum will be the total volume of titrant addedto the end point.

This method is carried out in the present invention by the provision ofmeans for measuring with great accuracy the amount of titrant added to asample and then by accumulating a digital count corresponding to themeasured volume. As the titrant is added, the measured potential acrossthe electrodes follows curve 10 in FIG. 1 and its first derivativefollows curve 14 in FIG. 2. The total amount of titrant added isaccumulated until the first derivative of the potential reaches theselected threshold value at point 28 (FIG. 2). From this point throughthe actual end point and to the second threshold point 30, only one-halfof the measured volume count is added to the previous total; at point30, both the titration and the count are stopped. The accumulated valueis then equal to the total volume of titrant added up to the end point16, thus giving a direct reading of the end point. Since the accuracy ofthis technique depends on the symmetry of the first derivative potentialcurve in the area of interest, it is desirable to set the thresholdvalue 26 as near the peak of the curve as possible. However, variationsin electrode sensitivity, random electrode potential fluctuations, andthe like establish a practical limit for reliable operation.

Referring now to the diagrammatic illustration of FIG. 4, there isillustrated in diagrammatic form a system and apparatus for carrying outthe half-count technique of the present invention. Accordingly, there isillustrated at 40 a sample cell or cup which is designed to receive asample 42 of the material which is to be titrated. The sample mayinclude any solvents or other materials necessary to the carrying out ofthe: titration, as is known in the art. Preferably, the cell willinclude a suitable stirring mechanism such as the magnetic stirrer 44which will serve to agitate the mixture and keep it uniform during thetitration. The stirrer may include bar 46 of magnetic material which maybe inserted in the cup and rotated or otherwise moved in the bottom ofthe cup by stirrer 44, again as is conventional.

The apparatus further includes a precision burette 48 which is driven bythe rotation of a micrometer screw 50 to deliver metered quantities oftitrant by way of a valve 52 and a feed tube 54 to the sample cell. Themicrometer screw 50 is operated by a suitable drive motor 56 and drivegear 58 to advance or retract the burette piston in accordance with theoutput of a motor control circuit 60. Preferably, a two-speed,reversible drive motor is used to permit the burette to be advanced at arapid rate until the inflection point of the titration curve isapproached, at which time the speed is reduced so as to add titrant tothe sample at a very slow rate through the end point. The motorpreferably is reversible to permit the burette to draw in a supply oftitrant from a suitable reagent supply source 62, by way of inlet valve64 and supply tubing 66.

In order to provide an accurate measure of the volume of titrant addedduring operation of the burette, a counting mechanism is connected tothe micrometer screw. As illustrated, this mechanism may take the formof a perforated disc mounted on the end of screw 50 and rotatabletherewith. The perforations in the disc are spaced equally around thedisc 70 at equal radial distances, and a photocell arrangement 72 isprovided adjacent the surface of the disc to provide an output pulse aseach perforation passes the photocell. Each output pulse thuscorresponds to the rotation of disc 70 through a prescribed number ofdegrees, and thus corresponds to the injection of a prescribed amount oftitrant through tube 54 into the sample cell 40, thereby providing adigital count corresponding to the volume of titrant dispensed by theburette. Since the count is proportional to the number of disc holesscanned, the initial position of the burette piston is unimportant, aslong as there is sufficient titrant in the burette to carry out acomplete titration.

Each output pulse from the photocell arrangement 72 is fed through anamplifier 74 to a Schmitt trigger 76. This trigger circuit generates asquare wave output pulse which is fed through a gating circuit 78 to acount accumulator 80 which provides on a suitable display device 82 anindication of the total end point volume delivered by the burette in anyone titration.

As is known in potentiometric titrations, a pair of electrodes 84 and 86are immersed in the sample material 42 which is to be titrated. Thestructure and material of such electrodes is Well known in the art, withthe present device contemplating the use of a glass-calomel or similarelectrode pair. A voltage potential will exist between the two spacedelectrodes in accordance with the composition of the sample and its pHvalue, and this potential is applied by way of lines 88 and 90 to anamplifier 92. The amplified signal is appliPd by way of line 94 to anetwork 96 for electrically obtaining the first derivative thereof. Asis known, a derivative network may take the form of an amplifier 98 anda parallel RC circuit consisting of resistor 100 and capacitor 102connected across the amplifier. The output of network 96 will be thefirst derivative of the changing potential appearing across electrodes84 and 86, and will take the form of curve 14 in FIG. 2. This firstderivative voltage is applied by way of line 104 to the input of Schmitttrigger network 106. A threshold setting means 108, which may be apotentiometer or the like, is provided to establish the trigger pointfor network 106 so that when the value of the potential applied by wayof line 104 reaches a specified value, the Schmitt trigger will producean output on line 110; this output will remain as long as the firstderivative of the electrode potential is above the threshold value.Thus, Schmitt trig ger 106 produces an output through the inflectionpoint of the titration, from points 28-30 on the curve 14 of FIG. 2.

The output signal from the Schmitt trigger is applied by way of line 110to suitable control logic circuitry 112 (to be described) which, inturn, produces an output signal on line 114 which is fed by way of line116 to the gate circuit 78. This output signal shifts the gate to ahalf-count mode whereby only alternate input pulses from Schmitt trigger76 will be passed to the accumulator 80. In this manner, count pulsesrepresenting only one-half of the actuaI volume of titrant added betweenpoints 28 and 30 of the first derivative curve are fed to accumulator80. The signal on line 114 is also fed to the motor control circuit 60to insure that the drive motor operates at its slow speed during thiscritical time of the titration. At the end of the output signal fromSchmitt trigger 106, the control logic 112 shuts down the drive motor 56by way of line 118, thus end- .ing the titration. The count value in theaccumulator may then be indicated on display 82 to provide a directreading of the volume of titrant added to obtain the end point of thetitration.

Briefly, then, the system of FIG. 4 provides a digital count of thestandard titrant added to the sample from the precision burette using,for example, a unit of one microliter per count. The sample potential isobtained from an appropriate electrode pair, and the first deriva tiveis derived from this analogue value by electrical means. As thederivative voltage reaches a predetermined threshold level, a controlcircuit switches the counting path so that only one-half of the unitscounted are sent to the count storage, or accumulator. Thus, as thetitration proceeds through the inflection area, only one-half of theadditional titrant is recorded. Finally, as

- the titration curve again flattens out and the first derivcarries, asin the system of FIG. 4, a disc 70 which may be perforated as previouslydescribed, or which may carry a plurality of alternating transparent andopaque sections 124 and 126, respectively. In this embodiment, themicrometer screw is driven through a suitable drive gear 58 by means ofeither a high speed drive motor 128 or a low speed drive motor130.-Rotation of the mi-' crometer screw to advance the plunger in theburette ejects the reagent fluid through feed tube 54 into the samplecell 40, as previously described. At the same time, rotation of thescrew-turns the disc 70 so that the alternate transparent and opaquesections pass between the upper and lower legs of a suitable sensingdevice 132. Sensor 132 may, for example, incorporate a light sourcemounted within an upper leg portion 134, and a photoelectric cellmounted within a lower leg portion 136. When an opaque section 126 ofthe disc is interposed between the light source and the photocell, nooutput is provided; however, when the disc rotates so that a transparentportion 124 is interposed between the upper and lower legs, thephotocell produces an output signal which appears on line 138 forapplication to a suitable amplifier 140. It will be apparent that theopaque and transparent portions illustrated on disc 70 are merelydiagrammatic, and that various other configurations may be used inccordance with known methods of converting the analogue value of shaftrotation into a digital pulse. The sensor 132 is designed to produce anoutput pulse for each advance of the disc, and thus of the micrometerscrew, through a predetermined angle. Since each such advance ejects apredetermined amount of reagent fluid from the burette, the outputpulses on line 138 will provide a direct count of the volume of reagentsupplied to the sample cell 40. A convenient value has been found to beone pulse output for each microliter of reagent dispensed.

The output signals amplified by amplifier 140 are fed to a Schmitttrigger 142, activating the trigger to produce a single output pulse ofpredeterminedamplitude which is applied by way of line 144 to one inputof a count gate 146. The pulse on line 144 is also applied to aflip-flop 148 which produces an output on line 150 for alternate inputpulses, thereby feeding one-half of the pulses on line 144 to a secondinput of the count gate.

The count gate 146 is a logic circuit which serves to regulate thepassage of counting pulses from the Schmitt trigger to its output line152, the state of the logic determining whether each of the pulses online 144 will produce a corresponding output pulse on line 152 orwhether only the alternate input pulses from line 150 will appear on theoutput line. In the former state,

the gate is in a full count mode, while in the latter state it is in ahalf-count mode.

The output pulses appearing on line 152 are applied to a suitablecounter which may, for example, consist of a plurality of cascadedcounters 154, 155, 156 and 157 which accumulate the pulses and produceoutputs which correspond respectively to the units, tens, hundreds andthousands of pulses received from the count gate. The counters may bestandard binary devices, each of which produces a binary output inaccordance with the number of counts received. The outputs of counters154-157 are applied to corresponding converter and display units 160,161, 162 and 163 which serve to convert the digital outputs toconventional base-ten numbering which may then be displayed, as by Iilluminated lamps or the like, or may be printed or otherwisepermanently recorded. It will be noted that a selected output of eachcounter is connected to the input of the following counter to effect thecascading arrangement. Thus, one output of counter 154 is connected byway of line 166 to the input of counter 155, one output of counter isconnected to the input of counter 156 by way of line 167 and one outputof counter 156 is connected to the input of counter 157 by way of line168, in a manner known in conventional counter networks.

A delivery selector network 170 is connected by way of lines 172-175 toselected stages in each of the counters 154-157 to' form, in effect, amultiple position switch which is responsive to a predetermined count toproduce an initial delivery pulse on line 176. A preselected number ofcounts after the initial delivery pulse appears, a permit signal isapplied by the delivery selector to its output line 178. These twopulses are provided to facilitate the titration operation by speeding upthe addition of titrant until the inflection point on the titrationcurve is approached and to prevent premature energization of thehalf-count mode. Since with most samples being tested, the approximateend point is known, it is possible to preselect a count (or volume oftitrant) which will be near this inflection point. In the presentdevice, the fast drive motor 128 is operated in the initial part of thetitration to add a predetermined amount of titrant, and when this isdone the initial delivery pulse turns off the fast drive motor andenergizes the slow drive motor 130, reducing the speed at which titrantis added to the sample. When titrant is added at a fast rate, a largeamount of electrical noise generally occurs in the sample cell, and itis difficult to measure with any accuracy the potential in the celluntil the quantity of titrant so added has been thoroughly mixed withthe sample. Therefore, the delivery selector 170 provides a delay time,during which titrant is added slowly and the sample is vigorouslystirred so that the electrical noise quiets down, before accuratemeasurements of cell potential are to be made by the electrodes. Thisdelay time may, for example, be approximately 200 counts at the slowrate, after which a permit signal is produced on line 178 which arms thesystem so that it will then respond to a threshold potential in thesample cell. This arrangement permits the titration to be carried outrelatively quickly, while at the same time preventing the system fromreacting to a noise signal that might exceed the threshold value andprematurely end the titration.

The logic circuitry which shifts the system from the fast drive motor tothe slow drive motor and which allows it to respond to a thresholdsignal may take many forms, but in the present invention it comprisestwo pair of conventional flip-flop circuits interconnected asillustrated in FIG. 5. The flip-flops 180 and 182 provide the switchinglogic for controlling drive motors 128 and 130, while flip-flops 184 and186 provide the switching logic for the threshold sensing mechanism.

F lip-flop 180 is of conventional type, having two output lines 188 and190, one of which will have a 0 output and the other of which will havea l or positive voltage output. In its normal, or reset, condition,

to flip, or set the unit, shifting it from its normal state to a setstate where line 188 carries a 1 output and line 190 carries a output.The flip-flop stays in this condition until a signal is received oninput 194 which flops the circuit back to its reset, or normal state. Ahold input 196 is also provided which serves to inhibit the flip-flopand prevent, it from changing state.

A start switch 198, which is provided for initiating a titration, isconnected to the set input 192 of flip-flop 180 by way of line 199. Thisswitch may be automatically or manually operated, depending upon thetype of system in which the present invention is incorporated, and issupplied by a suitable operating voltage from a DC power supply such asthat illustrated at 200. 7

Output line 188 of flip-flop 180 is connected to a set input 202 offlipflop 182, which is similar to flip-flop 180 and of conventionalconstruction. Output line 190 leads from flip-flop 180 to the hold input203 of flipflop 182 to inhibit operation of flip-flop 182 as long asflip-flop 180 is in the reset, or normal condition. Line 190 also leadsto an input 204 of the count gate 146 and to the input of a fast motorcontrol gate 206 which serves to control the operation of the drivemotor 128.

Flip-flop 182'has a first outputwhich, in its normal condition, carriesa 0 signal, and which is-connected to line 196 leading to the inhibitinput of flip-flop 180. The second output from flip-flop 182, whichnormally carries a 1 signal, is connected by way of line 208 to the holdinput of the count flip flop 184, inhibiting the setting of thatflip-flop as long as a 1 appears on line 208. Line 208 is also connectedby way of line- 210 to an input 212 of count gate 146 and to the inputof a slow motor control gate 214. This latter gate responds to a 0signal on line 210 to energize the slow motor 130; thus the setting offlip-flop 182 turns on the slow motor and releases flip-flop 184. Alsoconnected to line 210 is a restart switch 216 which permits the slowdrive motor to be manually operated, if desired.

The set input of the count flip-flop 184 is connected to the permit line178 leading from th delivery selector 170, so that flip-flop 184 will beshifted to its set condition upon receipt of a signal from selector 170if that signal occurs after flip-flop 182 has been set, and the holdsignal this removed from line 208. The 1 output of flip-flop 184 isconnected by way of line 218 to the hold input of the count flip-flop186, thereby inhibiting flip-flop 186 until flip-flop 184 is set by thepermit signal.

The set and reset inputs to flip-flop 186 are connected to output lines220 and 222, respecctively, of

the threshold signal Schmitt trigger 76 described with respect'to FIG.4. As has been explained, the electrodes 84 and 86, which are immersedin the sample contained in cell 40, produce a potential whichisproportional to the pH value of the sample. This potential isamplified in amplifier 92 and differentiated in the derivative network96 to produce an electrical signal similar to that illustrated by thecurve 14 of FIG. 2 during the course of the titration. When the outputof the differential network 96 reaches a predetermined level, theSchmitt trigger 76 is tired to produce a square wave signal ofpredetermined amplitude and of a length dependent upon the length oftime that the derivative value remains above the threshold level. Apotentiometer 224 or the like may be used to preset the threshold level.

The leading edge of a square wave output from the Schmitt trigger isapplied as a positive-going set signal by way of line 220 to theflip-flop 186, causing it to shift from its normal state to produce a 0output on output line 225 and a 1 output signal on output line 226. Thispositive going voltage on line 226 is applied to the final input of thecount gate 146 to shift the gate to its halfcount mode, and is appliedto the reset input 228 of flip-flop 182.

Referring now briefly to FIG. 6, the count gate 146 is illustrated infurther detail as consisting of an array of five OR logic circuits 230,231, 232, 233 and 234. Each of these OR gates is responsive to thepresence of a l signal at any one of its inputs to produce a 0 outputsignal. Thus, if a 1 appears on either line 204 or 212, which areconnected to the inputs of OR gate 230, the output of this gate on line236 will be a 0. On the other hand, 0 inputs on lines 204 and 212 willresult in a 1 output on line 236. In similar manner, 0 signals on inputlines 144 and 226 will result in OR gate 231 producing a 1 signal on itsoutput line 238 and similarly results in a 1 signal on the output line240 of OR gate 232. Again, if a 0 signal exists on both lines 150 and240 leading to the OR gate 234, a 1 signal will appear on its outputline 242. Lines 236, 238 and 242 provide the inputs to the OR gate 233and the presence of a 1 signal on any one of these lines results in a 0signal on output line 152.

FIG. 7 illustrates a typical OR gate such as the gate 233 wherein theinput lines236, 238 and 242 are connected to the base of a gatingtransistor 244. When no input appears on any of lines 236, 238 or 240,the transistor is non-conductive and the B+ voltage appears on outputline 152. However, if an input signal is applied to any of the threeinput lines, transistor 244 becomes conductive and line 152 goes toground potential, thereby producing a 0 on the output line.

The operation of a typical titration system may now be described withreference to FIGS. 5 and 6. Initially, the count gate 146 and thecounters .1 54-157 are reset to O and the flip-flops 180, 182, 184 and186 are reset to their normal, or rest, condition wherein their outputlines carry 0 and 1 signals, as indicated in the drawings. A samplematerial is placed in cup 40, and the delivery selector 170 is set toadd a predetermined volume of titrant to the sample under control of thehigh speed motor. The start button 198 is then depressed, producing apulse at input 192 of flip-flop 180, thereby reversing the outputs ofthis unit. A 0 signal now appears on line 190, which is fed to theinhibit input of flip-flop 182, to one of the inputs of OR gate 230(FIG. 6), and to the motor control gate 206. The 0 input at the gate 206energizes the fast drive motor 128 which begins to rotate micrometerscrew 50 and disc by means of gear mechanism 58, dispensing titrant fromburette 48 at a predetermined volume per unit of rotation.

The rotation of disc 70' produces a series of output pulses from thephotoelectric sensor 132, each pulse corresponding to a unit of titrantdispensed. These pulses are applied by way of Schmitt trigger 142 andline 144 to one of the inputs of OR gate 231 (FIG. 6), producing at thatinput a square wave input alternating between the 0 and 1 level. Thesignal on line 144 is also applied through flip-flop 148 where alternateinput signals set and reset it. One of the outputs of flip-flop 148 isconnected by way of line to one of the inputs of OR gate 234, producingat this input a square wave signal altermating between the 0 and 1 levelat one-half the frequency of the count signal on line 144. The

Schmitt trigger 142 continues to produce square wave output pulses aslong as the disc 70 is'rotated by either the fast or the slow drivemotors.

The positive, or 1 signal, applied to line 188 at the start of thetitration is applied to the set input 200 of flip-flop 182. However,this flip-flop does not change state because of the hold signal appliedby the O on line 190. This hold signal effectively makes the set inputresponsive to the trailing edge of a positive pulse; i.e., when thesignal on line 188 returns to flip-flop 182 will shift.

Under this condition, with the fast motor operating to drive theburette, the count gate 146 operates to provide an output pulse on line152 for each' input pulse that appears on line 144. Referring now toFIG. 6, OR gate 230 is blocked by a positive signal appearing on line212 from flip-flop 182. Since flip-flop 1861s still in its initialcondition, line 226 carries a 0 signal and accordingly OR gate 232produces a 1 on line 240, blocking OR gate 234. The 0 signal on line 226does not block OR gate 231, and thus the alternating input count signalson line 144 will produce alternating l and 0 signals on its output line238. Since OR gate 234 is blocked, a 0 appears on line 242; similarly, a0 appears on line 236 and neither or these lines will block OR gate 233.Thus, the alternating pulse on line 238 corresponding to the full countfrom Schmitt trigger 142 will appear on the output line 152. This fullcount pulse is applied to counter 154 (FIG. 5) and in known mannercounters 154-157 accumulate a count corresponding to the number ofpulses received.

When a preselected count is reached, the delivery selector switch passesthat count to the initial delivery line 176 which pulses the input 194of the fast motor flip-flop 180, returning it to its initial condition.This returns a 1 signal to line 190, which removes the hold fromflip-flop 182 and allows it to shift; the return to O of the signal online 188 accomplishes this shift. The signal on line 190 is applied tothe count gate 146, blocking OR gate 230, and at the same time disablesthe motor control gate 206 to turn off the fast drive motor. Whenflip-flop 182 shifts, it places a 1 signal on line I 196 which thenholds the fast motor flip-flop 180 in its initial condition, andprevents the fast motor 128 from being energized. A 0 signal now appearson line 208 which is fed by way of line 210 to a hold input 211 whichprevents the reset input 228 on flip-flop 182 from responding to theleading edge of a positive input pulse. The signal on line 210 is alsoapplied by way of line 212 to the OR gate 230 and to the input of themotor control gate 214, thereby energizing the slow drive motor. Underthis condition, the count gate con-- tinues to produce full count pulseson its output line 152, and the counter continues to operate as before.

After a delay time of about 200 counts, which provides sufficient timefor the large volume of titrant added to the sample to be thoroughlymixed and the resultant electrical noise to have quieted down, thedelivery selector produces a signal on the permit line 178 which isapplied to the set input of flip-flop 184. This flip-flop is inhibitedby the positive signal that normally exists on line 208, but since thatsignal was removed when the slow motor was turned on, the permit signalshifts flip-flop 184. This places a 0 signal on line 218, and releasesthe flip-flop 186 so that it is capable of responding to a thresholdsignal from Schmitt trigger 76.

Count gate 146 is unaffected by the permit signalon line 178, and thefull count from Schmitt trigger 142 remains on output line 152. Theaddition of titrant to the sample material continues, with the burettebeing driven by the slow drive motor 130, and the voltage acrosselectrodes 84 and 86 approaches the inflection point on the curve ofFIG. 1 while the first derivative thereof follows curve 14 of FIG. 2 andapproaches the threshold point 28, which has been established by thesetting of potentiometer 224. When the threshold point is reached,Schmitt trigger 76 fires and produces a positive going pulse on line 220which shifts flip-flop 186. A 0 signal now appears'on line 225 and isfed to a hold input on flip-flop 186, keeping the flip-flop in thiscondition until the trailing, or negative going, edge of the thresholdpulse appears on line 222. The signal now on output line 226 is fed tocount gate 146 and to the reset input 228 of flip-flop 182. However,flip-flop 182 does not shift at this time because of the hold signalapplied to line 211, and the slow motor continues to run.

As will be seen from FIG. 6, the 1 signal applied to line 226 blocks ORgate 232, shifting its outputto 0. At

' the same time, the 1 signal on line 226 is applied to OR gate 231 andblocks that gate also, preventing the passage of full count signals fromline 144 to line 152. With a 0 now appearing on line 240, the output ofOR gate 234 will follow the half-count signal appearing on line 150,thereby producing a half-count on line 242. With gates 230 and 231blocked, a 0 signal results on each of lines 236 and 238, and OR gate233 will follow the half-count pulses on line 242, thereby feeding thishalf-count signal to line 152. As before, the counters 154-157accumulate the pulses fed to them by way of line 152.

if The half--count operation continues through the end point of thetitration (FIG. 2) until the threshold point 30 is again reached, atwhich time Schmitt trigger 76 turns off. This produces a pulse on line222 which corresponds to the trailing edge of the threshold pulse, andwhich returns flip-flop 186 to its original condition, placing a 0signal on line 226. This return to 0 appears as a negative going signalon line 228 which resets flipflop 182 and turns off the slow motor 130.The 0 signal on line 226 is applied to OR gate 232 which then produces al on its output 240 to block gate 234 and prevent any half-count pulseson line 150 from passing to the output line 152. However, it is notedthat when both motors are off, disc 70' will stop rotating, and nopulses normally will appear on line 144 or on line 150. With a 0 on line226 and a O on line 144, OR gate 231 produces a 1 on line 238 and blocksOR gate 233, further preventing output signals from appearing on line152.

The total count now appearing in the counters 154-157 may be convertedto decimal form and displayed by converter and display units -163. Ashas been explained, the count accumulated and displayed in the mannerdescribed above will represent the total volume of titrant added to thesample up to the end point of the titration. This is because the fullcount has been recorded up to threshold point 28 on the curve 14, andone-half of the volume added between points 28 and 30 were added to thatfirst total. Because of the symmetry of curve 14 above the thresholdpoint, onehalf of the count between points 28 and 30 will give the endpoint 16 with a high degree of accuracy.

The fast drive motor 128 may also be used to fill burette 48 from asuitable supply, and to this end the motor is provided with means foroperating it in a reverse direction. This means includes a manuallyoperable refill switch 250 which is in series with a normally closedbottom limit switch 252 responsive to the position of the plunger in theburette. Alternating current power from a source 254 is applied to thedrive motors 128 and 130 by way of the normally closed top limit switchcontact 256 and a line 258 whereby operation of either of the motorcontrol gates 206 or 214 allows the corresponding motor to run in itsforward direction, until the burette plunger reaches its top limit,indicating that the supply of titrant .has been depleted. At this time,the top limit switch 256 opens and prevents further operation of themotor until the burette is refilled. A manual deliver switch 260 isprovided to allow the fast drive motor to be operated in a forwarddirection, if desired. A magnetic stirrer motor 262 is connected acrosssource 254 by means of an on/off switch 264 which may be manuallyorautomatically operated.

The basic system described with respect to FIG. can be refined in manyways, and additional features may be added to permit the use of thissystem in a continuing and automatic monitoring of an industrial processwherein the results of a series of titrations are used for qualitycontrol purposes. In such a system, the use of the optional fast drivemotor feature described herein is of particular use, for it permits amajor portion of the titrant to be added initially to each sample, whenit is known that the samples will vary only slightly in characteristicsand thus speeds up the titration procedure. As described, this rapidaddition is followed by a brief settling to permit proper mixing andallow accurate measurements; it will be apparent that the slow motor maybe used throughout the procedure, if desired.

A practical machine for carrying out such continuous analysis hasbeenreduced to practice and has been found to provide a highlysignificant improvement in quality control. With the developed machine,it now becomes possible to obtain the result of a titration of a sampledrawn from a production line every 6 minutes, for example, automaticallyand without the need for skilled laboratory personnel. This compareswith the former method of such monitoring wherein at least three trainedtechnicians were required to manually titrate samples taken periodicallyfrom the production material. With three highly trained persons, it wasonly possible to obtain results from 12 or 15 titrations during an8-hour shift, and no results were obtained during the remaining l6 hoursof a days production run. On the other hand, the present machine may beoperated on a 24-hour-per-day basis, with results that are virtually asaccurate as those obtained in the manual methods previously used whileeliminating the need for skilled operators. With 24-hour monitoring ofan industrial process through the use of this machine, a far superiorcontrol can be maintained over production processes.

An automatic system of this type may, for example, be constructed with alarge turntable adapted to receive a large number of sample cups spacedaround its circumference. To provide additional testing stations, it maybe desired to provide two circumferential rows so that by duplicatingthe burette, motor controls, counters and the like, two titrations canbe carried on at one time. Preferably, the system would include indexingmeans for rotating the table periodically to bring the sample cupssuccessively into position below the burette where the titration takesplace. In such an automatic system, the electrodes placed in the samplecup would have to be movable, and for this purpose may be located on asuitable elevator. By properly timing the duration of each titratingstep, and by providing a suitable number of sample receptacles on theturntable, a system can be operated automatically with only a minimalamount of attention. Thus, an attendant would take a sample of thematerial to be tested and place it in a cup together with the solventsnecessary to the performance of the titration. The sample cup may thenbe placed in an appropriate position on the tumtable so that as thetable indexes, the sample will be carried thereon for a timesufficiently long to enable the solvent and the sample to reach a stablecondition (i.e., the sample may be carried by the turntable for an houror more before the titration actually takes place). When a cup isindexed under the burette, the electrodes are lowered into it and amagnetic stirrer begins operation, rotating a stirring bar within thecup. The titration then proceeds as described herein above, and upon itscompletion the cup is indexed away from the titrating station. Automaticmeans may be provided to lift the cup out of the turntable and empty it,with the stirring bar being recovered for future reuse.

A system for operating a turntable device of the foregoing type isgenerally illustrated in FIG. 8. Although this illustration isdiagrammatic, it will be seen from this how the circuitry of FIG. 5 maybe adapted to more complex automatic titration apparatus. As shown inFIG. 8B, two burettes 270 and 271 are illustrated, the first being forsample cups carried on a first row around the periphery of the turntableand the other being for a second row of samples. As has been described,the output of the burette 270 is monitored by a sensor 272, the outputof which is fed through a Schmitt trigger 274 to produce count pulsescorresponding to the volume of titrant dispensed. These pulses are fedto a count gate 276. The electrodes 280 in the sample cell beingtitrated produce an output which is differentiated, with thedifferential voltage operating a trigger circuit 282 at a predeterminedthreshold value. The output of the trigger is fed to the count gate 276by way of line 284. As before, a signal on line'284 shifts the countingrate from a full count to ahalf-count when the threshold point of thetitration is reached. The output of the count gate is fed by way of line286 to a channel A counter, or accumulator, 288 where the countcorresponding to the volume of titrant dispensed is stored for displaypurposes. As before, a delivery selector switch 290 is connected to thecounter to produce an output on line 292 when the initial high speeddelivery has been completed, in those installations where such aninitial delivery is appropriateQand to provide on line 294 apermit-signal which arms the system for response to the threshold signalfrom trigger 282. A control switch network 296, which consists of theflip-flop networks illustrated in FIG. 5, responds to the variouscontrol signals to operate the motor-driven burette at the appropriatespeed, by way of motor control network 298, and to regulate theoperation of count gate 276. The channel B burette 270' operates insimilar manner, and the corresponding elements of channels A and B aresimilarly numbered, with the channel B elements being primed.

The operation of the turntable, electrode positioning elevators,stirrers and the like is controlled by a programmer which may, forexample, include a series of cam follower switches operated by camsmounted on the shaft of a suitable drive motor. Such a programmer isillustrated in FIG. 8A as comprising a programmer motor 310 and aplurality of turntable control cams and switches 312 driven therebythrough a mechanical drive shaft 314. The programmer motor operates as aclock, and regulates the overall operation of the automatic titrator. Y

Alternating current is supplied to the system from a source 316 througha master on/off switch 318. Power is applied by way of transformer 320to an indexing lamp 322 which is located adjacent the turntable 322. Anaperture is provided at each sample station around the circumference ofthe turntable so that when the table is properly positioned for atitration, light from lamp 322 will pass through the correspondingapertures and fall on photocell devices 326 and 328. The output fromphotocell 326 is fed through amplifier 330 to the coil 332 of a stirrerrelay, thereby closing its normally open contact 332 and applying powerfrom source 316 to a stirrer motor 334. This motor may be provided witha starter 336, and when activated serves to rotate a magnetic stirrerbar located within the sample cup positioned at the titrating station tostir the sample. Also connected to line 334 is a magnet catcher 340,including a catchermotor 342 which is used to recover the magneticstirrer bar when the titration is over and the sample is discarded.

The output of photocell device 328 is fed by way of line 344 to a gatecircuit 346 to provide an indication when the turntable is properlypositioned so that the titration can go forward. A pair of solventcontainer switch contacts 348 and 350 are responsive to the fluid levelin the container which dispenses solvents into the sample containersbefore they reach the titration station. When the container isempty, theswitches reverse condition and halt the operation of the device. Thegate also provides an input to the turntable control network 312 whenthe turntable is properly positioned to regulate the cup and stirrerremoval equipment and the electrode raising and lowering elevators.

The main power supply to the system is provided by way of line 354 andstart button 356 which ismanually closed to provide current to the coilof a main power relay 360. Upon energization of the coil of relay 360,its normally open contact 360 is closed so that the main current path isfrom line 354 through the normally closed stop button 362, the normallyclosed A burette switch 364 andthe normally closed B burette switch 364so that contact 360' acts as a self-holding contact for the relay.Contact 360" is also closed by energization of relay 360 'so that poweris supplied to the turntable control cams and switches 312 by way of andthe like are not affected by electrical transients and noise. Theprogrammer motor 310 operates through cams in the control array 312 torefill the burettes with titrant by operating their respective fastdrive motors in a reverse direction, as has been explained. Uponcompletion of this, the refill switch opens and the cams operate theelectrode elevators to lower the electrodes and titration tubes into thesample cell which is at the titration station and which is being stirredby motor 336. Continued rotation of programmer 310 then causes cam 374to shiftits corresponding contacts 374', applying a positive going pulsethrough line 376 to a reset circuit 378 to remove the reset clamp andthrough line 380 to the control flip-flops 296 and 296 to start thetitration. The photoelectric counters, reset to 0, begin to countmicroliters of titrant as they are dispensed to. each sample, and when apredetermined count is reached the corresponding flip-flops and controlnetworks 296 and 296 are reset to change the appropriate burettes fromrapid to slow delivery. An additional 200 counts later, the deliveryselectors 290 and 290' again activate the control switches 296 and 296'to permit the first derivative circuits in each channel to becomeactive. As the pH value of each sample approaches its maximum rate ofchange, indicating that its end point is approaching, the increasingfirst derivative voltage reaches the threshold point at which it shiftsthe counting rate to one-half the number of counts detected by thecorresponding sensors 272 or 272. Finally, as the pH change in thesample decreases, the decrease in the first derivative again operates onthe control switches to stop the count at the threshold value and tostop the burette motor. This sequence and counting action occursindependently for the two channels A and B. When both titrations havebeen completed, and the counts showing the amount of titer added to thesample to reach the end point have been stored in the correspondingaccumulators, the program cycle resumes. The programmer motor may bestopped during the titration and then restarted in response to theoperation of the flip-flop which shuts off theburette motor, forexample, or the cycle may be established in the programmer so that themotor will continue to run, with the next step in the cycle occurring apredetermined length of time after the start of titration. In eitherevent, the next step in the cycle is for the programmer motor 310 todrive printout cam 382 to shift its corresponding contacts and therebystart a clock pulse generator 384. The clock has three phases, the firstbeing a rest state which is its reset condition, and the other two beingtrigger and operate states which produce alternate output signals. Thus,a train of trigger pulses appear on output line 386 and a train ofalternate operate pulses appear on output line 388. The trigger pulsesare applied to a conventional shift register 390 which steps oneposition for each trigger pulse received, with each position producing acorresponding output signal which is used to gate information to abinary to decimal converter network 392. This converter produces anoutput which is a decimal digit 0-9 corresponding to the binaryinput'that it receives.

A plurality of turntable position switches, which may be microswitchesactuated by coded pins located at each station of the turntable, areindicated generally at 394. The particular combination of microswitchesclosed by these coded pins controls the energization of selected gatesin the gate network 396, and the first two outputs of the shift registertransfer this information to the converter 392. These first two pulsesfrom the shift register each transfer one digit of the turntableposition to the converter, and the intervening operate pulse on line 388causes the converter to feed that data to a printer 398. This printermay be a standard, heavy-duty adding machine wherein the -9 digit keysare mechanically operated by corresponding solenoids, the propersolenoid being selected by the output from converter 392. After the twodigits corresponding to turntable position have been entered in theprinter, the shift register then operates to transfer the accumulatedcount from the channel A counter 288 to the converter 392. The counteris arranged so that each pulse from the shift register transfers inbinary form one of the decimal digits making up the count. Thus, thethird pulse from the shift register transfers the units count in theaccumulator 288, the fourth pulse transfers the tens, the fifth pulsetransfers the hundreds and the sixth pulse transfers the thousands digitto the converter where the alternating operate pulses on line 388 againtransfer these numbers to the printer. The next output pulse from theshift register operates the printer to provide a printed readout of theturntable position and the accumulated count.

After two idle counts from the shift register, which are provided toallow time for the printer to complete its operation, the channel Baccumulator 288' is similarly read out and printed, the print signalbeing applied by way of line 400 to a printer solenoid 402. The finaloutput fromthe shift register 390 is applied by way of line 404 to thereset circuit 378 which resets all of the circuits to the initialcondition, ready for the next titration. If desired, a hold button 406may be provided to interrupt the reset line 404 so that the system willremain in its current condition, thereby permitting an interim printoutby operation of a manual print button.

Upon completion of the printout and resetting, the programmer motor 310drives the indexing cams and switches indicated generally at 410, thusactivating an indexing motor controller 412 to'energize an index motor414. At the same time, the motor operates the elevator cam to raise theelectrodes, in both sample cups. When this operation has been completed,the elevator switches 416 and 418 are closed,,allowing the index motorto be energized to rotate the turntable to the next position. Theprogram motor then operates the cup emptying equipment to discard theused sample, and when this operation has been completed the system isready to begin another cycle.

Numerous other features may be provided in a system of this type, as isknown in the art of automatic titrators. Thus, signal lights may beprovided to give a continuous indication of the operational state of thesystem, and various manually operated switches may be provided tooverride the automatic systems described herein. Further, safety relaysresponsive to undervoltage conditions and the like together withsuitable warning lights may be provided, but all of these features arewell known and their application to a system utilizing the presentinvention will be apparent to those of skill in the art.

Although the present invention has been described with respect to asystem for determining the end point of a titration wherein thepotential curve has a single break, the second application of thistechnique occurs in the case where there are two inflection points inthe pl-l-volume of titrant curve. in such cases, it is required todetermine the volume of titrant added between the two inflection points.Such a curve is illustrated in FIG. 9' at 420, where first and secondinflection points 422 and 424 are generally indicated. As before, thepoints of maximum inflection 426 and 428 are of interest, and it isrequired to determine the volume of titrant added between these twopoints.

FIG. 10 illustrates the first derivative of the curve of FIG. 9, andillustrates that two peaks are generated by this curve, one occurring ateach inflection point, as at 422' and 424. The first derivative curve430 has again been found to be substantially symmetrical above athreshold value indicated by line 432, and this threshold value can beagain used to regulate a counting circuit so that the desired volume isobtained. To provide the desired volume reading, additional or modifiedlogic circuits are required so that the systems of FIGS. 5 or 8 willoperate in the following manner. As the first derivative curve 430increases toward the threshold value, no count is accumulated, for thisvolume of titrant is not of interest. However, at the threshold value atpoint 434 in FIG. 10, the count gate is activated to produce ahalf-count, as has previously been described. This half-countcontinuesuntil the curve falls below the threshold value, at point 436. However,instead of shutting down the system at this point, the count gate isshifted to the full count mode and a full count is accumulated until thecurve 430 increases above the threshold value a second time, at point438. Again, the system shifts to a half-count mode until at point 440the first derivative falls below the threshold value, at which time thesystem is shut down The total count accumulated between points 434 and440 then represents the volume of titrant added between the points ofmaximum inflection at 426 and 428. For this type of measurement, onlythe slow drive motor is used. Thus, the start button would be utilizedto operate-the slow motor, rather than the fast motor, and the deliveryselector would be energized to continuously provide a permit signal,thereby arming the flip-flop which is responsive to the first derivativesignal. In this manner, the circuit is responsive to the first output ofa derivative circuit which occurs when the threshold is reached, but themotor is not turned off when the signal returns to that threshold level.Instead, the output of the derivative circuit merely returns the countgate to its full count until the threshold is again reached. By asuitable arrangement of flip-flops, or like switching networks, the slowmotor control is made responsive to the second decrease of th'e firstderivative output to the threshold level, and at that time the motor isturned off and the count is terminated. If desired, this may be modifiedby energizing the fast motor during the full count, but where theoverall time period for the titration is not too great, the use of thefast motor drive is not necessary.

A potentiometric titrator has been built and operated in accordance withthe herein disclosed half-count concept, and has been foundsatisfactorily to meet the requirements of industry and of the AmericanSociety of Testing Material for its industrial monitoring procedures.Thus, for example, the manufacture of nylon polymer has been monitored,with test samples taken from the product line for testing in theautomatic titrator described with respect to FIG. 8. In one such test,

each sample consisted of approximately two and onehalf grams of nylonpolymer which was placed in a sample cell, or cup, and the sample wastitrated to determine the amine end group of the nylon polymer. Amagnetic stirring bar was placed in the cup and the cup placed in theturntable, the remainder of the test was fully automatic, so thatskilled testing personnel were not required.

When the turntable was indexed to the appropriate station. solvent wasautomatically metered into the cup containing the nylon polymer, andapproximately 60 ml. of a menol solvent was added. The sample wasdissolved and stirred as the turntable continued to be periodicallyindexed so that titration of samplesin preceding cups could be carriedout. The sample dissolved in approximately 1-% hours, but the number ofpositions and the indexing rate of the turntable were so arranged thatthe given sample cup was not-carried into position for titration forapproximately l- /2 hours after the solvent had been added. When the cupmoved into the titrating position, the electrodes and the titrant feedtube were lowered into the cell and the stirring motor was energized.

The sample was titrated with an alcoholic solution of perchloric acid,the fast motor operating to add titrant at a high rate of speed until1,200 microliters of titrant had been added; thereafter, the slow motoroperated to microliters was printed. Results calculated from this Ianalysis showed 57.6 meq of amine end per kg. The electrodes were thenraised, the turntable indexed and the spent solution discarded togetherwith the sample cup, the magnetic stirrer being retained for furtheruse. A second sample was taken from the same production run and titratedmanually, with a graphical analysis being made of the end point. Theresult of this test showed 57.4 rneq. of amineend per kg. 7

A second example of the use of the present machine was the determinationof the combined acidic content of cellulose acetate in accordance withASTM methods. In this example, a sample of about two grams of celluloseacetate were placed in a sample cup, and the.

cup was placed on the turntable of the subject titrator. At the solventstation, 100 milliliters of acetone solvent were added and the samplewas allowed to dissolve. Thereafter, 68 milliliters of 0.5 normal sodiumhydroxide (aqueous solution) was added, thereby forming regeneratedcellulose and permitting suponification of the actual end group.

After a delay period of 30 minutes, the. sample cup was indexed to adiluting station, where 100 ml. of hot, demineralized water, at about180F, was metered into the sample cup. After stirring, the sample wastitrated in accordance with the above-described half-count method, usinga standard hydrochloric acid solution. The total count was then printedout, and the sample discarded. The printout showed a total volume of22.35 ml of titrant added to the end point, as compared to a value of22.42 ml. obtained through the manual graphical method described above.

As an illustration of the use of the present method in a double endpoint titration, a test was run to determine manual and graphicalmethods, which showed 82.!

"meq/kg. c

ple. The selected sample, which was of a convenient and practical sizein accordance with normal techniques, was placed in solution by theaddition of benzyl alcohol, in accordance with the prescribed method.The sample so prepared was placed in a sample cup on the turntable and10 ml of methanolic perchloric acid was added to bind the amine endgroups. The amount of acid so added was in excess of that required forthe binding, thereby providing a solution having an excess of perchloricacid, plus the dissolved polymer, plus the carboxyl end groups, so thatthe carboxyl groups could be titrated.

The sample was indexed to the titration station, and was titrated withan alcoholic solution hydroxide. The titrant was added under the controlof the slow motor with the differentiating circuit armed by the permitsignal to be responsive to the threshold of the first derivative signal.No measurement of the titrantvolume was recorded, stored or displaceduntil the start of the halfcount at the threshold of the firstpotentiometric break. This break was that of the excess perchloric acid,and the half-count mode continued through the end point of this break.The first derivative returned to the threshold level, after 35p. 1 oftitrant had been added and the system shifted to a full count. The slowmotor continued to operate to add titrant until the secondpotentiometric break was reached. At the threshold value of the firstderivative at the second break, which is that of the carboxyl endgroups, the system shifted back to the half-count, SOS .tl. having beenadded to this time. The carboxyl end groups were then titrated throughtheir end point and when the first derivative curve again turned to thethreshold value, the motor was shut down and the titration ended.

The total count of 897u1. was then printed out, giving the total amountof titerrequired to neutralize, the carboxyl end groups; that is, theamount of titrant added between the end points of the two potentiometricbreaks. This result was computed to give a value of 82.6 meq/kg. Thisvalue compared with a similar calculation made of a similar sample byFrom the foregoing, it will be seen that the present invention isadaptable to use in carrying out virtually any titration in which thereis a potentiometric break. The break can be skewed or very broad, but aslong as the curve above the threshold is approximately symmetrical therecan be an accurate titration, for a small amount of non-symmetry in thisarea only introduces a negligible error. Any titration which cansuccessfully be performed by standard or developed potentiometrictechniques can be carried out by the present system, with more precisemeasurements being available than could previously be obtained byautomatic methods, the results of the present system being equivalent tothose previously available only through laborious techniques involvingmanual plotting of the titration curves and calculation of the endpoint. Where, for example, quality control for monitoring industrialprocesses is desired, such techniques are unsatisfactory, for theyrequire too much time to perform. The present system not only automatessuch procedures, but also further speeds the titration by adding titrantduring a fast motor operation, particularly where the samples beingtested are known to be similar in characteristics. However, where thesamples may vary substantially in characteristics, a slow motor may beused to meter the titrant, or the fast motor may be used for a shortperiod of time to avoid overrunning the end point.

The system as described provides great flexibility, and it will beapparent to those of skill in the art that numerous modifications can bemade without departing from the true spirit and scope of the invention.For example, the disclosed method contemplates a halfcount mode wherealternate pulses are fed to the accumulator; however, it will beapparent that this halfcount can be obtained in numerous other wayswithout departing from the disclosed concept. For example, the

count occurring above the threshold point can be separately accumulatedat its full rate, and then divided in half by known data handlingtechniques before being added to the value accumulated prior to thethreshold. It will also be seen that since the information obtained bythe present system is in digital form, it is directly adaptable tocomputerizd data handling techniques, so that instead of the printeddisplay described herein, the information can be fed directly toconventionaldata handling machines for further processing, storage, usein a process control system for correcting any errors in the processthat might be detected by the titration, or the like. in view of theforegoing, it is desired that the description herein of preferredembodiments be taken as illustrative and that the true spirit and scopeof the invention be limited only by the following claims.

What is claimed is:

1. A method of determining the end point of a potentiometric titration,comprising the steps of:

adding titrant to a sample at a measured rate;

measuring changes in the pH potential of said samples as titrant isadded and determining the first derivativeof said potential; measuringthe full amount of titrant added to said sample until said firstderivative reaches a preset value; and

thereafter measuring one-half the titrant added through the endpoint ofsaid titration until said first derivative returns to said preset value.

2. The method of claim 1, wherein the measurement of titrant added tosaid sample includes:

generating electrical signals which represent unit quantities of titrantdelivered to said sample; and accumulating said signals.

3. The method of claim 2, wherein said electrical signals are digitalrepresentations of the quantity of titrant delivered, said digitalsignalsbeing accumulated to provide a continuous record of the quantityof titrant added to said sample.

4. The method of claim 3, further including the step of halting saidtitration when said first derivative returns to said preset value.

5. The method of claim 4, wherein the measurement of titrant added tosaid sample further includes:

accumulating all of the said digital signals generated before said firstderivative reaches said preset value; and

accumulating one-half of the said digital signals thereafter generated.

6. The method of claim 5, further including the step of displaying avalue represented by said accumulated digital signals to obtain thevolume of titrant added to said sample to reach the said end point.

7'. The method of claim 6, wherein the step of displaying a valueincludes the steps of summing the digital signals accumulated beforesaid preset first derivathe amount of titrant added to reach tive valueis reached with the digital signals thereafter accumulated, the value ofsaid sum representing the total volume of titrant added to reach saidend point.

8. A method of determining the end point of potentiometric titrationcomprising:

adding titrant to a sample at a controlled rate;

measuring the amount of titrant added to said sample;

generating electrical signals representing the measured amount oftitrant;

measuring changes in the potential of said sample as titrant is added;

obtaining the first derivative of said potential;

accumulating said electrical signals at a first rate until said firstderivative reaches a predetermined value; and

thereafter accumulating said electrical signals at a second rate untilsaid derivative returns to said value.

9. The method of claim 8, further including selecting said predeterminedvalue sufficiently near the maximum value of said first derivative thatsaid derivative is substantially symmetrical about said maximum valueabove said predetermined value.

10. The method of claim 9, wherein the said second rate of accumulationof said electrical signals is onehalf the said first rate ofaccumulation.

11. The method of claim 10, further including the step of halting saidtitration when said first derivative returns to said predeterminedvalue, and thereafter obtaining directly from the accumulated electricalsignals the end point of said titration.

12. A method of determining the amount of titrant added to a sample toreach the end point of potentiometric titration, comprising:

supplying titrant to a sample at acontrolled rate;

generating at least one digital electrical pulse for each unit quantityof titrant added to said sample; measuring changes in the potential ofsaid samples as titrant is added; obtaining a variable signalrepresenting the first derivative of saidpotential, said variable signalhaving a maximum value at'the end point of said titration;

determining a threshold value of said first derivative signal;

counting the pulses generated during said titration;

accumulating the full count of said pulses until said first derivativesignalreaches said threshold value and thereafter accumulating one-halfthe count of said pulses; and

halting said titration after said first derivative signal passes throughsaid maximum value and returns to said threshold value.

13. The method of claim 12, further including supplying said titrant tosaid sample at a first rate until a predetermined quantity has beendispensed, and thereafter supplying titrant at a second rate.

14. The method of claim 13, further including the step of reading theaccumulated pulse count to provide a direct indication of the volume oftitrant added to said sample to reach said end point.

15. The method of claim 14, including the step of selecting saidpredetermined threshold value sufficiently near the maximum value ofsaid first derivative that said derivative is substantially symmetricalabout said maximum value and above said threshold.

16. The method of determing the amount of titrant added between thefirst and second equivalence points of a complex sample having twopotentiometric breaks in the titration curve, including:

supplying titrant to said sample at a controlled rate;

generating at least one digital electrical pulse ,for

each unit quantity-of titrant added to said sample; measuring changes inthe potential of said sample as titrant is added;

obtaining a variable signal representing the first derivative of saidpotential, said variable signal having a maximum value for eachequivalence point of said titration; determining a threshold value ofsaid first derivative signal, said threshold value being selected to besufficiently near each of said maximum values of said first derivativethat said derivative is substantially symmetrical about each maximumvalue and above said threshold;

counting the pulses generated during said titration;

accumulating one-half said count while said variable signal exceeds saidthreshold value and accumulating the full value of said count betweensaid first and second equivalence points while said variable signal isbelow said threshold value, the total count so accumulated representingthe amount of titrant added to carry said sample from said first to saidsecond equivalence points.

17. In a potentiometric titrator for determining the equivalence pointof a sample, apparatus for providing a direct and accurate measure ofthe volume of titrant added to said sample in reaching said equivalencepoint, comprising:

a sample cell for receiving a sample to be titrated;

means for supplying titrant to said sample cell;

means for generating electrical signals corresponding to the volume oftitrant supplied; means for measuring the electrical potential of saidsample and producing an output corresponding to the first derivative ofsaid potential; 7

means for storing all of said electrical signals until said firstderivative reaches a predetermined value and for thereafter storing onlya predetermined portion of said electrical signals; and

means responsive to said first derivative output for halting saidtitration when said first derivative returns to said predeterminedvalue. v

18. The apparatus of claim 17, further including means responsive tosaid first derivative output for producing a threshold signal when saidoutput reaches said predetermined value, said means for storingelectrical signals responding to the occurrence of said threshold signalto store only said predetermined portion of said electrical signals.

19. The apparatus of claim 18, further including means for reading outthe total value of said stored electrical signals to obtain the totalvolume of titrant supplied to reach said equivalence point.

20. The apparatus of claim 18, wherein said means for reading includesdisplay means.

21. The apparatus of claim 17, wherein said means for generatingelectrical signals includes pulse means for producing at least one pulseper unit volume of titrant delivered.

22. The apparatus of claim 21, wherein said means for storing electricalsignals comprises counter means for counting said pulses.

23. The apparatus of claim 22, wherein said means for storing electricalsignals includes gate means responsive to said first derivativeoutput,said gate means operating in a full count mode to deliver all ofsaid pulses to said counter means umtil said first derivative reachessaid predetermined value, said gate means thereafter operating in ahalf-count mode to deliver only alternate pulses to said counter means.I i 24. The apparatus of claim 23, wherein said gate means includesmeans responsive to said first derivative output for producing athreshold signal when said output reaches said predetermined value, anda count gate responsive to said threshold signal, said threshold signalshifting said count gate from a full count mode to a half-count mode.

25. The apparatus of claim 24, further including readout means forobtaining a direct indication of the accumulated count in said counter,and thus of the total volume of titrant added to said sample.

26. The apparatus of claim 17, wherein said means for supplying titrantincludes burette means for delivering metered quantities of titrant tosaid cell, and electric motor means for driving said burette at acontrolled speed.

27. The apparatus of claim 26, wherein said means for generatingelectric signals comprises means responsive to the operation of saidburette to generate at least one electrical pulse for each unit volumeof titrant delivered by said burette.

28. The apparatus of claim 27, wherein said burette is operated by arotary, motor-driven shaft, and said pulse generating means comprisesphotoelectric means reponsive to the rotation of said shaft forproducing a plurality of pulses for each rotation of said shaft.

29. The apparatus of claim 27, further including control means for saidelectric motor means for selectively driving said burette at one of twospeeds.

30. The apparatus of claim 27, wherein said means for storing saidelectrical signals comprises counter means for receiving said generatedelectrical pulses and g for accumulating a count corresponding to thenumber of pulses received.

31. The apparatus of claim 30, wherein said means for storing saidelectrical signals further comprises count gate means having a fullcount mode and a halfcount mode, said count gate shifting from one modeto the other when said first derivative reaches said predeterminedvalue.

32. The apparatus of claim 31, further including readout means fordisplaying the count accumulated in said counter and to display thevolume of titrant added to said sample.

33. The apparatus of claim 17, wherein said means for measuring theelectrical potential of said samples includes electrode means forimmersion in said sample, said electrodes producing a potentialdifference which is a measure of the pH of said sample, and circuitmeans connected to said electrodes for producing the first derivative ofsaid electrode potential difference.

34. The apparatus of claim 33, further including trigger meansresponsive to a predetermined value of said first derivative, saidtrigger means producing an output threshold signal as long as said firstderivative exceeds said predetermined value.

35. The apparatus of claim 34, wherein said means for storing saidelectrical signals includes count gate means responsive to saidthreshold signal, said count gate means operating in a full count modeto store all of said electrical signals in the absence of said thresholdsignal and operating in a half-count mode to store only alternate onesof said electrical signals in the presence of said threshold signal.

36. The apparatus of claim 35, wherein said means for generatingelectric signals comprises burette means for delivering meteredquantities of titrant to said cell, and means responsive to theoperation of said burette to generate at least one electrical countpulse for each unit volume of titrant delivered by said burette.

37. The apparatus of claim 36, wherein said means for generatingelectric signals further comprises second trigger means for supplyingsaid electrical count pulses to said count gate means,

38. The apparatus of claim 37, wherein said means for storing saidelectrical signals comprises counter means responsive to count pulsespassed by said count gate, said count gate being operative in its fullcount mode to pass all of said count pulses to said counter means, andbeing operative in its half-count mode to pass alternate ones of saidcount pulses.

39. in a potentiometric titrator for automatically determining thevolume of titrant added to a sample to reach the end point of atitration;

a sample cell for receiving a sample to be titrated;

burette means for delivering metered quantities of titrant to said cell,and electric motor means for driving said burette; motor control logiccircuit means for regulating the speed of said electric motor means;

means responsive to the operation of said burette to generate at leaseone count pulse for each unit volume of titrant delivered by saidburette;

counter means for receiving said count pulses and for accumulating acount corresponding to the number of pulses received;

count gate means interposed between said means for generating countpulses and said counter means, said count gate having a full countmodewherein all of said generated count pulses are passed to said countermeans and having a half-count mode wherein only one-half of saidgenerated count pulses are passed to said counter means;

means for measuring the potential of said sample during titrationthereof, andcircuit means for producing the first derivative of saidpotential;

means responsive to a predetermined value of said first derivative toproduce a threshold signal; and circuit means for applying saidthreshold signal to said count gate to shift said count gate from a fullcount mode to a half-count mode and for holding said count gate in thehalf-count mode as long as the value of said first derivative exceedssaid predetermined value.

40. The apparatus of claim 39, wherein said motor control logic circuitmeans includes a delivery selector network responsive to said countermeans, said delivery selector network producing an initial deliverysignal upon delivery of a predetermined volume of titrant to saidsample, said motor control circuit being responsive to said initialdelivery signal to change the speed of said electric motor means,whereby an initial quantity of titrant can be added to said sample at adifferent rate than the rate at which the remainder of titrant is added.

41. The apparatus of claim 40, further including inhibit circuit meansfor inhibiting the production of said threshold signal, said deliveryselector network including means for producing a permit signalsubsequent to said initial delivery and upon delivery of an additionalpredetermined volume of titrant, said permit signal disabling saidinhibit circuit means.

42. The apparatus of claim 41, wherein said motor means includes a highspeed and a low speed motor,

and wherein said motor control logic circuit means includes switchingmeans for selectively energizing said motors, said switching meansinitially energizing said high speed motor and being responsive to saidinitial delivery signal to de-energize said high speed motor andenergize said low speed motor.

43. The apparatus of claim 42, further including means responsive to thetermination of said threshold signal for disabling said count gate andfor deenergizing said electric motor means.

44. The apparatus of claim 43, further including means for reading outthe total count accumulated in said counter means to obtain the totalvolume of titrant delivered to said sample to reach said end point.

2. The method of claim 1, wherein the measurement of titrant added tosaid sample includes: generating electrical signals which represent unitquantities of titrant delivered to said sample; and accumulating saidsignals.
 3. The method of claim 2, wherein said electrical signals aredigital representations of the quantity of titrant delivered, saiddigital signals being accumulated to provide a continuous record of thequantity of titrant added to said sample.
 4. The method of claim 3,further including the step of halting said titration when said firstderivative returns to said preset value.
 5. The method of claim 4,wherein the measurement of titrant added to said sample furtherincludes: accumulating all of the said digital signals generated beforesaid first derivative reaches said preset value; and accumulatingone-half of the said digital signals thereafter generated.
 6. The methodof claim 5, further including the step of displaying a value representedby said accumulated digital signals to obtain the volume of titrantadded to said sample to reach the said end point.
 7. The method of claim6, wherein the step of displaYing a value includes the steps of summingthe digital signals accumulated before said preset first derivativevalue is reached with the digital signals thereafter accumulated, thevalue of said sum representing the total volume of titrant added toreach said end point.
 8. A method of determining the end point ofpotentiometric titration comprising: adding titrant to a sample at acontrolled rate; measuring the amount of titrant added to said sample;generating electrical signals representing the measured amount oftitrant; measuring changes in the potential of said sample as titrant isadded; obtaining the first derivative of said potential; accumulatingsaid electrical signals at a first rate until said first derivativereaches a predetermined value; and thereafter accumulating saidelectrical signals at a second rate until said derivative returns tosaid value.
 9. The method of claim 8, further including selecting saidpredetermined value sufficiently near the maximum value of said firstderivative that said derivative is substantially symmetrical about saidmaximum value above said predetermined value.
 10. The method of claim 9,wherein the said second rate of accumulation of said electrical signalsis one-half the said first rate of accumulation.
 11. The method of claim10, further including the step of halting said titration when said firstderivative returns to said predetermined value, and thereafter obtainingdirectly from the accumulated electrical signals the amount of titrantadded to reach the end point of said titration.
 12. A method ofdetermining the amount of titrant added to a sample to reach the endpoint of potentiometric titration, comprising: supplying titrant to asample at a controlled rate; generating at least one digital electricalpulse for each unit quantity of titrant added to said sample; measuringchanges in the potential of said samples as titrant is added; obtaininga variable signal representing the first derivative of said potential,said variable signal having a maximum value at the end point of saidtitration; determining a threshold value of said first derivativesignal; counting the pulses generated during said titration;accumulating the full count of said pulses until said first derivativesignal reaches said threshold value and thereafter accumulating one-halfthe count of said pulses; and halting said titration after said firstderivative signal passes through said maximum value and returns to saidthreshold value.
 13. The method of claim 12, further including supplyingsaid titrant to said sample at a first rate until a predeterminedquantity has been dispensed, and thereafter supplying titrant at asecond rate.
 14. The method of claim 13, further including the step ofreading the accumulated pulse count to provide a direct indication ofthe volume of titrant added to said sample to reach said end point. 15.The method of claim 14, including the step of selecting saidpredetermined threshold value sufficiently near the maximum value ofsaid first derivative that said derivative is substantially symmetricalabout said maximum value and above said threshold.
 16. The method ofdeterming the amount of titrant added between the first and secondequivalence points of a complex sample having two potentiometric breaksin the titration curve, including: supplying titrant to said sample at acontrolled rate; generating at least one digital electrical pulse foreach unit quantity of titrant added to said sample; measuring changes inthe potential of said sample as titrant is added; obtaining a variablesignal representing the first derivative of said potential, saidvariable signal having a maximum value for each equivalence point ofsaid titration; determining a threshold value of said first derivativesignal, said threshold value being selected to be sufficiently near eachof said maximum values of said first derivative that said derivative issubstantially symmetrical about each maximum value and above saidthreshold; counting the pulses generated during said titration;accumulating one-half said count while said variable signal exceeds saidthreshold value and accumulating the full value of said count betweensaid first and second equivalence points while said variable signal isbelow said threshold value, the total count so accumulated representingthe amount of titrant added to carry said sample from said first to saidsecond equivalence points.
 17. In a potentiometric titrator fordetermining the equivalence point of a sample, apparatus for providing adirect and accurate measure of the volume of titrant added to saidsample in reaching said equivalence point, comprising: a sample cell forreceiving a sample to be titrated; means for supplying titrant to saidsample cell; means for generating electrical signals corresponding tothe volume of titrant supplied; means for measuring the electricalpotential of said sample and producing an output corresponding to thefirst derivative of said potential; means for storing all of saidelectrical signals until said first derivative reaches a predeterminedvalue and for thereafter storing only a predetermined portion of saidelectrical signals; and means responsive to said first derivative outputfor halting said titration when said first derivative returns to saidpredetermined value.
 18. The apparatus of claim 17, further includingmeans responsive to said first derivative output for producing athreshold signal when said output reaches said predetermined value, saidmeans for storing electrical signals responding to the occurrence ofsaid threshold signal to store only said predetermined portion of saidelectrical signals.
 19. The apparatus of claim 18, further includingmeans for reading out the total value of said stored electrical signalsto obtain the total volume of titrant supplied to reach said equivalencepoint.
 20. The apparatus of claim 18, wherein said means for readingincludes display means.
 21. The apparatus of claim 17, wherein saidmeans for generating electrical signals includes pulse means forproducing at least one pulse per unit volume of titrant delivered. 22.The apparatus of claim 21, wherein said means for storing electricalsignals comprises counter means for counting said pulses.
 23. Theapparatus of claim 22, wherein said means for storing electrical signalsincludes gate means responsive to said first derivative output, saidgate means operating in a full count mode to deliver all of said pulsesto said counter means until said first derivative reaches saidpredetermined value, said gate means thereafter operating in ahalf-count mode to deliver only alternate pulses to said counter means.24. The apparatus of claim 23, wherein said gate means includes meansresponsive to said first derivative output for producing a thresholdsignal when said output reaches said predetermined value, and a countgate responsive to said threshold signal, said threshold signal shiftingsaid count gate from a full count mode to a half-count mode.
 25. Theapparatus of claim 24, further including readout means for obtaining adirect indication of the accumulated count in said counter, and thus ofthe total volume of titrant added to said sample.
 26. The apparatus ofclaim 17, wherein said means for supplying titrant includes burettemeans for delivering metered quantities of titrant to said cell, andelectric motor means for driving said burette at a controlled speed. 27.The apparatus of claim 26, wherein said means for generating electricsignals comprises means responsive to the operation of said burette togenerate at least one electrical pulse for each unit volume of titrantdelivered by said burette.
 28. The apparatus of claim 27, wherein saidburette is operated by a rotary, motor-driven shaft, and said pulsegenerating means comprises photoeleCtric means reponsive to the rotationof said shaft for producing a plurality of pulses for each rotation ofsaid shaft.
 29. The apparatus of claim 27, further including controlmeans for said electric motor means for selectively driving said buretteat one of two speeds.
 30. The apparatus of claim 27, wherein said meansfor storing said electrical signals comprises counter means forreceiving said generated electrical pulses and for accumulating a countcorresponding to the number of pulses received.
 31. The apparatus ofclaim 30, wherein said means for storing said electrical signals furthercomprises count gate means having a full count mode and a half-countmode, said count gate shifting from one mode to the other when saidfirst derivative reaches said predetermined value.
 32. The apparatus ofclaim 31, further including readout means for displaying the countaccumulated in said counter and to display the volume of titrant addedto said sample.
 33. The apparatus of claim 17, wherein said means formeasuring the electrical potential of said samples includes electrodemeans for immersion in said sample, said electrodes producing apotential difference which is a measure of the pH of said sample, andcircuit means connected to said electrodes for producing the firstderivative of said electrode potential difference.
 34. The apparatus ofclaim 33, further including trigger means responsive to a predeterminedvalue of said first derivative, said trigger means producing an outputthreshold signal as long as said first derivative exceeds saidpredetermined value.
 35. The apparatus of claim 34, wherein said meansfor storing said electrical signals includes count gate means responsiveto said threshold signal, said count gate means operating in a fullcount mode to store all of said electrical signals in the absence ofsaid threshold signal and operating in a half-count mode to store onlyalternate ones of said electrical signals in the presence of saidthreshold signal.
 36. The apparatus of claim 35, wherein said means forgenerating electric signals comprises burette means for deliveringmetered quantities of titrant to said cell, and means responsive to theoperation of said burette to generate at least one electrical countpulse for each unit volume of titrant delivered by said burette.
 37. Theapparatus of claim 36, wherein said means for generating electricsignals further comprises second trigger means for supplying saidelectrical count pulses to said count gate means.
 38. The apparatus ofclaim 37, wherein said means for storing said electrical signalscomprises counter means responsive to count pulses passed by said countgate, said count gate being operative in its full count mode to pass allof said count pulses to said counter means, and being operative in itshalf-count mode to pass alternate ones of said count pulses.
 39. In apotentiometric titrator for automatically determining the volume oftitrant added to a sample to reach the end point of a titration; asample cell for receiving a sample to be titrated; burette means fordelivering metered quantities of titrant to said cell, and electricmotor means for driving said burette; motor control logic circuit meansfor regulating the speed of said electric motor means; means responsiveto the operation of said burette to generate at lease one count pulsefor each unit volume of titrant delivered by said burette; counter meansfor receiving said count pulses and for accumulating a countcorresponding to the number of pulses received; count gate meansinterposed between said means for generating count pulses and saidcounter means, said count gate having a full count mode wherein all ofsaid generated count pulses are passed to said counter means and havinga half-count mode wherein only one-half of said generated count pulsesare passed to said counter means; means for measuring the potential ofsaid sample during titration thereof, and ciRcuit means for producingthe first derivative of said potential; means responsive to apredetermined value of said first derivative to produce a thresholdsignal; and circuit means for applying said threshold signal to saidcount gate to shift said count gate from a full count mode to ahalf-count mode and for holding said count gate in the half-count modeas long as the value of said first derivative exceeds said predeterminedvalue.
 40. The apparatus of claim 39, wherein said motor control logiccircuit means includes a delivery selector network responsive to saidcounter means, said delivery selector network producing an initialdelivery signal upon delivery of a predetermined volume of titrant tosaid sample, said motor control circuit being responsive to said initialdelivery signal to change the speed of said electric motor means,whereby an initial quantity of titrant can be added to said sample at adifferent rate than the rate at which the remainder of titrant is added.41. The apparatus of claim 40, further including inhibit circuit meansfor inhibiting the production of said threshold signal, said deliveryselector network including means for producing a permit signalsubsequent to said initial delivery signal and upon delivery of anadditional predetermined volume of titrant, said permit signal disablingsaid inhibit circuit means.
 42. The apparatus of claim 41, wherein saidmotor means includes a high speed motor and a low speed motor, andwherein said motor control logic circuit means includes switching meansfor selectively energizing said motors, said switching means initiallyenergizing said high speed motor and being responsive to said initialdelivery signal to de-energize said high speed motor and energize saidlow speed motor.
 43. The apparatus of claim 42, further including meansresponsive to the termination of said threshold signal for disablingsaid count gate and for de-energizing said electric motor means.
 44. Theapparatus of claim 43, further including means for reading out the totalcount accumulated in said counter means to obtain the total volume oftitrant delivered to said sample to reach said end point.